American Institute of Mathematical Sciences

May  2012, 6(2): 121-130. doi: 10.3934/amc.2012.6.121

On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$

 1 Department of Mathematics, KTH, S-100 44 Stockholm 2 Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, I-06123 Perugia

Received  January 2011 Revised  August 2011 Published  April 2012

It is proved that for every integer $n=2^k-1$, with $k\geq5$, there exists a perfect code $C$ of length $n$, of rank $r=n-\log(n+1)+2$ and with a trivial symmetry group. This result extends an earlier result by the authors that says that for any length $n=2^k-1$, with $k\geq5$, and any rank $r$, with $n-\log(n+1)+3\leq r\leq n-1$ there exist perfect codes with a trivial symmetry group.
Citation: Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$. Advances in Mathematics of Communications, 2012, 6 (2) : 121-130. doi: 10.3934/amc.2012.6.121
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References:
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